Sixth Mississippi State Conference on Differential Equations and
Computational Simulations.
Electron. J. Diff. Eqns., Conference 15 (2007), pp. 1127.
Boundary conditions for the EinsteinChristoffel formulation
of Einstein's equations
Douglas N. Arnold, Nicolae Tarfulea
Abstract:
Specifying boundary conditions continues to be a challenge in numerical
relativity in order to obtain a long time convergent numerical simulation of
Einstein's equations in domains with artificial boundaries.
In this paper, we address this problem for the EinsteinChristoffel
(EC) symmetric hyperbolic formulation of Einstein's equations linearized
around flat spacetime. First, we prescribe simple boundary conditions
that make the problem well posed and preserve the constraints.
Next, we indicate boundary conditions for a system that extends the
linearized EC system by including the momentum constraints and whose
solution solves Einstein's equations in a bounded domain.
Published February 28, 2007.
Math Subject Classifications: 35Q75, 35L50, 83C99.
Key Words: General relativity; Einstein equations; boundary conditions.
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Douglas N. Arnold
Institute for Mathematics and its Applications,
University of Minnesota, Minneapolis, Minnesota 55455, USA
email: arnold@ima.umn.edu
http://www.ima.umn.edu/~arnold 

Nicolae Tarfulea
Department of Mathematics, Purdue University Calumet
Hammond, Indiana 46323, USA
email: tarfulea@calumet.purdue.edu
http://ems.calumet.purdue.edu/tarfulea 
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